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Epsilon Cores of Games with Limited Side Payments: Nonemptiness and Equal Treatment

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  • Kovalenkov, Alexander
  • Wooders, Myrna Holtz

Abstract

We introduce the concept of a parameterized collection of games with limited side payments, ruling out large transfers of utility. With convexity of the payoff set of the grand coalition, we show that (1) a game with limited side payments has a nonempty epsilon-core and (2) when some degree of side-paymentness within nearly effective small groups is assumed and large transfers are prohibited, then all payoffs in the epsilon-core treat similar players similarly. A bound on the distance between epsilon-core payoffs of any two similar players is given in terms of the parameters describing the game. These results add to the literature showing that large games with small effective groups have the properties of competitive markets. For prior equal treatment results for large games see especially Wooders (1980,1994a,b), Shubik and Wooders (1982) and Wooders (1983, Theorem 3) available at http://www.warwick.ac.uk/fac/soc/Economics/wooders/.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 36 (2001)
Issue (Month): 2 (August)
Pages: 193-218

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Handle: RePEc:eee:gamebe:v:36:y:2001:i:2:p:193-218

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Web page: http://www.elsevier.com/locate/inca/622836

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  1. Peter J. Hammond, . "On f-Core Equivalence with General Widespread Externalities," Working Papers 95004, Stanford University, Department of Economics.
  2. Martin Shubik & Myrna Holtz Wooders, 1982. "Near-Markets and Market Games," Cowles Foundation Discussion Papers 657, Cowles Foundation for Research in Economics, Yale University.
  3. Le Breton, M. & Owen, G. & Weber, S., 1991. "Strongly Balanced Cooperative Games," G.R.E.Q.A.M. 91a09, Universite Aix-Marseille III.
  4. Wooders, Myrna Holtz & Zame, William R, 1984. "Approximate Cores of Large Games," Econometrica, Econometric Society, vol. 52(6), pages 1327-50, November.
  5. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
  6. Mas-Colell, Andreu, 1975. "A further result on the representation of games by markets," Journal of Economic Theory, Elsevier, vol. 10(1), pages 117-122, February.
  7. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
  8. Mas-Colell, Andreu, 1979. "A refinement of the core equivalence theorem," Economics Letters, Elsevier, vol. 3(4), pages 307-310.
  9. Kaneko, Mamoru & Wooders, Myrna Holtz, 1982. "Cores of partitioning games," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 313-327, December.
  10. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416.
  11. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-60, September.
  12. Kaneko, Mamoru & Wooders, Myrna Holtz, 1989. "The core of a continuum economy with widespread externalities and finite coalitions: From finite to continuum economies," Journal of Economic Theory, Elsevier, vol. 49(1), pages 135-168, October.
  13. Billera, Louis J., 1974. "On games without side payments arising from a general class of markets," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 129-139, August.
  14. Kaneko, Mamoru, 1982. "The central assignment game and the assignment markets," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 205-232, September.
  15. Garratt, Rod & Qin, Cheng-Zhong, 1997. "On a Market for Coalitions with Indivisible Agents and Lotteries," Journal of Economic Theory, Elsevier, vol. 77(1), pages 81-101, November.
  16. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
  17. Bennett, Elaine & Wooders, Myrna, 1979. "Income distribution and firm formation," Journal of Comparative Economics, Elsevier, vol. 3(3), pages 304-317, September.
  18. Shapley, Lloyd S & Shubik, Martin, 1969. "On the Core of an Economic System with Externalities," American Economic Review, American Economic Association, vol. 59(4), pages 678-84, Part I Se.
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Citations

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Cited by:
  1. Ehud Lehrer & Marco Scarsini, 2013. "On the Core of Dynamic Cooperative Games," Dynamic Games and Applications, Springer, vol. 3(3), pages 359-373, September.
  2. Allouch, Nizar & Wooders, Myrna, 2008. "Price taking equilibrium in economies with multiple memberships in clubs and unbounded club sizes," Journal of Economic Theory, Elsevier, vol. 140(1), pages 246-278, May.
  3. Wooders, M. & Selten, R. & Cartwright, E., 2001. "Some First Results for Noncooperative Pregames : Social Conformity and Equilibrium in Pure Strategies," The Warwick Economics Research Paper Series (TWERPS) 589, University of Warwick, Department of Economics.
  4. Wooders, Myrna, 2008. "Small group effectiveness, per capita boundedness and nonemptiness of approximate cores," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 888-906, July.
  5. Tovey, Craig A., 2010. "The instability of instability of centered distributions," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 53-73, January.
  6. Nizar Allouch & Myrna Wooders, 2004. "Price taking equilibrium in club economies with multiple memberships and unbounded club sizes," Cahiers de la Maison des Sciences Economiques b04109, Université Panthéon-Sorbonne (Paris 1).
  7. Myrna Wooders, 2010. "Cores of many-player games; nonemptiness and equal treatment," Review of Economic Design, Springer, vol. 14(1), pages 131-162, March.
  8. Myrna Wooders, 2009. "Market Games and Clubs," Vanderbilt University Department of Economics Working Papers 0919, Vanderbilt University Department of Economics.
  9. Wooders, Myrna H., 2001. "Some corrections to claims about the literature in Engl and Scotchmer (1996)," Journal of Mathematical Economics, Elsevier, vol. 36(4), pages 295-309, December.
  10. Allouch, Nizar & Wooders, Myrna, 2002. "Competitive Pricing In Socially Networked Economies," The Warwick Economics Research Paper Series (TWERPS) 639, University of Warwick, Department of Economics.

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